Question: Vanessa is 5 times as old as Kevin. Four years ago, Vanessa was 7 times as old as Kevin. How old is Vanessa now?
Explanation: We can use the given information to write down two equations that describe the ages of Vanessa and Kevin. Let Vanessa's current age be $v$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $v = 5k$ Four years ago, Vanessa was $v - 4$ years old, and Kevin was $k - 4$ years old. The information in the second sentence can be expressed in the following equation: $v - 4 = 7(k - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to solve our first equation for $k$ and substitute it into our second equation. Solving our first equation for $k$ , we get: $k = v / 5$ . Substituting this into our second equation, we get: $v - 4 = 7($ $(v / 5)$ $- 4)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $v - 4 = \dfrac{7}{5} v - 28$ Solving for $v$ , we get: $\dfrac{2}{5} v = 24$ $v = \dfrac{5}{2} \cdot 24 = 60$.